The motions of points, lines, and planes, embedded in a rigid body are expressed in a unified algebraic framework using a Clifford algebra. A Clifford algebra based displacement operator is addressed and its higher de...The motions of points, lines, and planes, embedded in a rigid body are expressed in a unified algebraic framework using a Clifford algebra. A Clifford algebra based displacement operator is addressed and its higher derivatives from which the coordinate-independent characteristic numbers with simple geometric meaning are defined. Because of the coordinate independent feature, no tedious coordinate transformation typically found in the conventional instantaneous invariants methods is needed.展开更多
基金This material is based upon work supported by the National Science Foundation under Grant No. DMI-0219859 and MSS-9301975.
文摘The motions of points, lines, and planes, embedded in a rigid body are expressed in a unified algebraic framework using a Clifford algebra. A Clifford algebra based displacement operator is addressed and its higher derivatives from which the coordinate-independent characteristic numbers with simple geometric meaning are defined. Because of the coordinate independent feature, no tedious coordinate transformation typically found in the conventional instantaneous invariants methods is needed.
